Answer:
\((-x,-9]\cup [5,x)\)The equations of two consecutive asymptotes of the function are \(x=0\) and \(x=2\pi \)The function is not a reflection over the \(x\)-axisHelpful informationThe general equation of a cosecant function is \(y=\sec (ax)\), where \(a\) is a constantThe vertical asymptotes of a cosecant function are of the form \(x=k\pi \), where \(k\) is an integerThe range of a cosecant function is \((-\infty ,-1]\cup [1,\infty )\)How to solveWrite the general equation of a cosecant function. Then, adjust the parameters of the function so that it matches the given conditions.
Step-by-step explanation:
Step 1Find the values of \(a\) and \(b\).Since the range of the cosecant function is \((-x,-9]\cup [5,x)\), it follows that \(a=2\).Since the asymptotes of the cosecant function are \(x=0\) and \(x=2\pi \), it follows that \(b=2\pi \).Step 2Find the equation of the cosecant function.Substitute \(a=2\) and \(b=2\pi \) into the general equation of a cosecant function.\(y=\sec (ax)\)\(y=\sec (2x)\)SolutionThe equation of the cosecant function is \(y=\sec (2x)\)......... HOPE IT WILL BE HELPFUL....
